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Face Recognition using Improved FFT Based Radon by PSO and PCA Techniques

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Abstract Face Recognition is one of the problems which can be handled very well using a Hybrid technique or mixed transform rather than single technique, it is a very well in terms of a good performance and a large size of the problem. In this paper we represent the using of the Fourier-Based Radon Transform which is improved by the Particle Swarm Optimization (PSO). PSO in this research is used to select the optimum directions (projection angles) that achieve a very high recognition rate and a fast computation. The number of directions selected using PSO is less than the number required by ordinary Radon. This leads to a small number of features. These number of features are reduced farther using PCA to produce a low number of features which used to represent faces in the database. Our method has been applied to ORL Database and achieves 100% recognition rate.

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Face Recognition using Improved FFT Based Radon by PSO and PCA Techniques

  1. 1. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 26 Face Recognition Using Improved FFT Based Radon by PSO and PCA Techniques Mr. Hamid M. Hasan Hamid2012net@gmail.com Electrical Eng. Dept. Basra University, college of Eng. Basra , Iraq Prof. Dr. Waleed A. AL.Jouhar Profwaleed54@yahoo.com Electrical Eng. Dept. Baghdad University, College of Eng. Baghdad , Iraq Dr. Majid A. Alwan Altimimee@yahoo.com Electrical Eng. Dept Basra University, college of Eng. Basra , Iraq Abstract Face Recognition is one of the problems which can be handled very well using Hybrid techniques or mixed transform rather than single technique. This paper deals with using of Radon Transform followed by PCA and LDA techniques for Face Recognition. The data used are 2D Face Images from ORL Database. The Radon Transform used is based on FFT slice theorem. The directions along which the Radon transform is performed are selected using PSO in order to achieve a good recognition rate. The best directions selected are less computation expensive as compared to the full set of directions and achieve good recognition rate. The PCA is used to reduce the dimension of the data produced by Radon Transform and the LDA is used to find a set of basis vectors which maximizes the ratio between-class scatter and within–class scatter. In order to verify our method many dataset partitioning scenarios into training set and testing set were conducted. And the maximum recognition rate achieved was 97.5%. Keywords: Face Recognition (FR), Radon Transform (RT), Fast Fourier Transform (FFT), Principal Component Analysis (PCA), Linear Discrimenant Analysis(LDA) and Particle Swarm Optimization (PSO). 1. INTRODUCTION Face recognition is one of the most important biometrics which seems to be a good compromise between actuality and social reception and balances security and privacy well. It has a variety of potential applications in information security law enforcement and access controls. Face recognition systems fall into two categories: verification and identification. Face verification is 1:1 match that compares a face images against a template face image. On the other hand face identification is 1: N problem that compares a probe face image against all image templates in a face database. Face recognition is a very difficult problem due to a substantial variations in light direction (illumination) , different face poses , diversified facial expressions , Aging (changing the face over time) and Occlusions (like glasses, hair, cosmetics). So the building of an automated system that accomplishes such objectives is very challenging. In last decades many systems with recognition rate greater than 90% has been done however a perfect system with 100% recognition rate remains a challenge. Face recognition algorithms are divided by [1, 2] into three categories as follows:
  2. 2. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 27 1. Holistic methods: These methods identify a face using the whole face images as input and extract the overall features. 2. Feature based methods: these methods used the local facial features for recognition (like eyes, mouths, fiducial points. etc.). 3. Hybrid methods: these methods used both feature based and holistic features to recognize a face. These methods have the potential to offer better performance than individuals. 2. A REVIEW OF THE RELATED 2-D FACE RECOGNITION TECHNIQUES Thomas Heseltine [3] investigated three appearance based approaches for face recognition which are the direct correlation method, the eignface method and fisherface method. the recognition error rate reported is 18% , 20.4% , 17.8% respectively . M. Chandra Mohan[4] they divide the face into four parts and evaluates the texture features in each part separately the texture features are derived from parameters with different orientations, this makes the face recognition easier and pose, illumination and rotation invariant. P.Abouzar [5] using WT (Wavelet) and DCT ( Discrete Cosine Transform) followed by PCA the proposed algorithm takes advantages of data reduction property of the three transforms. The Support Vector Machine (SVM) was used to classify the images into different classes and the error rate obtained is between 5%-7%. Zhan Shi[6 ] they extract a number of features from facial images through taking Trace Transform over different angular directions by using different trace functions then the features are projected into a lower dimensional subspace. The recognition rate achieved is 95% in ORL database. Laika Karsili [7 ] used a Radon Transform over the set of angles{0,60,120,180,240,300,360}, then the produced data was reduced using PCA this achieves 70% recognition rate for rank 1 and 95% for rank 4. Jamal A hmad [8] Investigated the effect of the step size for both the angle and the vector of the radon transform on the performance of a face recognition system based on PCA it is founded that step size of one for both produces recognition rate of 89%. ZHANG et al, [9] proposed a feature extraction method based on finite Radon transform (FRAT) then used soft threshold (ST) to select main FRAT coefficients. Finally 2DMMC was used to extract features for classification from main FRAT coefficients. They achieved 89.02% recognition rate on ORL database. Ergun Gumus et al [10] they used Eigenfaces (PCA) and Support Vector Machine (VSM) on ORL database they achieved recognition rate of 91,2% for PCA-AVM (RBF) Radial bases. Zhang Lin et al [11] used Radon Transform with multiwavelet and PCA on Infrared imaged faces and they achieved 95% classification accuracy with 70 element feature vector. Yuehui Chen et al [12] proposed using DCT and Hybrid Flexible Neural Tree which was evolved using PSO their experiment on ORL achieved 98.13% recognition rate . Jian Zhang , Xianyun Fei[13] they used the PSO in order to select the optimum discrimination eigenvectors of PCA and obtain the optimal recognition accuracy simultaneously they validate their method with ORL database with recognition rate of 96%. Dattatray V. Jadhao and Raghunath S. Holambe[14] they used Radon transform and Fourier transform for face recognition on ORL database and achieved recognition rate of 97.33% the images were classified on the nearest neighbor with 60 features .
  3. 3. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 28 Rabab M.Ramadan [15] used PSO to select the efficient features from DCT and DWT and apply their method on ORL with recognition rate 94.7% and 96.8% respectively . In this paper we used the Radon Transform which is improved by PSO to select the best directions. Then a data reduction is performed using the PCA. A classification basis vectors are derived using LDA which lead to a rank one recognition rate equal to 97.5% and the feature vector size is 35 items per class (person). 3. THE METHOD AND MATERIALS The method used in this paper for face recognition is depicted in figure (1). It consists the enrollment phase and the testing phase. In the enrollment phase the training set of images are transformed into Radon space using the Radon Transform. The set of directions (angles) along which the transform is performed were calculated using the Particle Swarm Optimization (PSO). Different sets of directions are shown in tables (1, 2, 3). The different sets are for different classifier parameters which yield a good estimated recognition rate. The data generated by Radon Transform are reduced using Principal Components Analysis (PCA). From those reduced data set (i.e. the most effective components) a set of basis vectors which maximizes the ratio between-class scatter and within–class scatter using Linear Discrimenant Analysis (LDA). One basis vector for each class (i.e. Person) is derived and stored in the data base. So for ORL Image database there are 40 basis vectors are stored regardless of the number of images used for each person in the training set. The length of the basis vector depends on the number of components selected by the PCA stage. In the testing phase the input image is transformed into the Radon space using that set of directions which were used in the enrollment phase. The PCA reduction is carried out as same as in the enrollment phase. The resultant vector is projected into the basis vectors stored in the data base that is by inner product method. The highest product value which must be higher than a predetermine threshold measures the similarity between the input image and the specified class. The method which is stated in this paper was evaluated using the ORL data base which contains photographs of faces taken at the Olivetti Research Laboratory in Cambridge between April 1992 and April 1994.There are 10 different images of 40 distinct subjects so there are 400 images in the data base. The images are grayscale with a resolution of 92 x 112. For some of the subjects, the images were taken at different times. There are variations in facial expression and pose variation about 20 degrees and there is some variation in scale of up to about 10%. There are some faces with glasses. Some images are shown in figure (2). In the following sections the discussion of each main part of the method of process is presented.
  4. 4. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 29 FIGURE 1: Block diagram for the recognition system. 3.1 Radon Transform There were many applications of Radon transform like Pose Estimation [17],Texture Analysis [18], X-ray crystallography and Nuclear Magnetic Resonance(NMR)[19], Image Matching for translation, rotation and uniform scaling Using Radon Transform[21]. Several definitions of the radon transform existed. A very popular form expresses lines is:- t ൌ x ‫כ‬ cosሺθሻ ൅ y ‫כ‬ sinሺθሻ ሺ1ሻ Where θ is the angle and t is the smallest distance to the origin of the coordinate system. The Radon transform for a set of parameters (t, θ) is the line integral through the image f(x, y), where the line is positioned corresponding to the value of (θ and t) in Equation (2). gሺt,θሻ ൌ ඵ fሺx, yሻδ൫t െ x cosሺθሻ െ y sinሺθሻ൯dx dy ሺ2ሻ ାஶ ିஶ In the above equation g(t,θ) is the Radon Transform of the f(x,y) function at a specified value of t and θ . The Radon transform can be calculated using FFT by applying the central-slice theorem [13] which is stated that the 1-D Fourier transform of the integral projection at angle θ is equal to the slice of the 2-D Fourier transform at the same angle. With the central-slice theorem the Radon transform can be computed equivalently with 2-D FFT, a Cartesian-to-polar mapping, and a 1-D FFT. The range of the θ is [0...179] and the range of the variable ( t ) depends on the dimension of the underling image. In our case the t is in the range [1...112] and θ range is [0...179] that is for full range directions. So each image is represented in Radon space as a vector of dimensions equal to (180 x112) = 20160. In our work a subset of θ is selected from the full range using Particle Swarm Optimization (PSO). The subset of θ values is selected according to the goodness of the recognition rate achieved as the objective function. Using different values of parameters used by the classifier a different subset are selected using PSO. Figure (3) shows a full range of θ Radon transform and figure (4) shows a subset of θ Radon transform. 3.2 Particle Swarm Optimization (PSO) PSO, first introduced by Kenny and Eberhart in 1995 [22], is one of the evolutionary computation technology based on swarm intelligence. In a PSO system each solution called a "particle", particles fly around in the search space of the problem to look for the optimal solution. Each particle adjusts its position according to the flying experience of its own and the experience of neighboring particles. Each particle updates its velocity and position using the following equation [23]:- Vi(k+1)=Vi(k)+c1* rand1( pbest(k) - Xi(k)) + c2* rand2( gbest(k) - Xi(k)) (3) Xi (k+1)=Xi(k) + Vi(k+1) (4) Where , Vi is called the velocity for particle i; Xi is represent the position of particle i ; Pbest is the best position of ith particle gbest is the global best position ; rand is random variable in [0,1]; c1 and c2 are the learning factors; w is called the inertia weight To search for optimal solution, each particle changes its velocity according to equation 3. The value of Vi is clamped to the range [Vmin, Vmax] to avoid excessive roaming of particle outside the search space. Then each particle moves to a new potential solution using equation 4. This process is repeated until a stopping criterion is reached. The above equations (4,5) are the basic
  5. 5. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 30 equations and not guarantee the global solution. Using those equations PSO may be trapped in local minima to avoid the local minima there are many variations and improvements to the basic equations have been suggested [24-37]. In this work we used the PSO in order to select the best set of directions (the values of θ) to be used in Radon transform. These set is selected from the full set of θ from 0ᵒ to 179ᵒ in step of 1 degree. There are 24 particles in the swarm are used with randomly selected values of θ. These particles moved and evolved towards the best positions that yield a good Recognition rate. The objective function was constructed in order to optimize both the recognition rate and the number of directions (θ) selected as well. Three sets are depicted by tables( 1 ,2,3) for three values of N which is the length of the features vector used by the classifier associated with objective function used. In our experiments, the set with N=60 was used. One thing that be mentioned about PSO is its convergence to a steady state of accepted recognition rate very quickly and in stable manner. 3.3 Feature Reduction Using (PCA) The PCA is a statistical method for reducing data dimensions [37,38]. In PCA the training data is used in obtaining the Eigen basis vectors. Then the training set R and testing set T are projected into those vectors. The PCA can be summarized by the following steps:- a. Calculate the mean M of the training set and subtract it from the training set: M ൌ ଵ ୬ ∑ R୧ ୬ ୧ୀଵ (5) For all training set perform R୧ ൌ R୧ െ M b. Calculate the Eigenvectors and Eigenvalues of the training set covariance matrix ܵ௧ S୲ ൌ R . RT (6) and pick the Eigen vectors corresponding to the N largest Eigen values of ܵ௧. These construct the N principal components matrix ( V). c. The Basis vectors matrix (U) is constructed as: U ൌ V . RT (7) d. The reduced feature vector is calculated for training and testing data as: WR ൌ R . U (8) WT ൌ T . U (9) The mean M must be subtracted from the testing data T also. Many experiments were conducted using different numbers of Eigenvectors (N ) between (10-60) and the performance are reported in figure(5,7 ). 3.4 Linear Discrimenant Analysis (LDA) The LDA finds a set of basis vectors which maximizes the ratio between-class scatter and within –class scatter [37]. Given N samples of C classes, let Ni be the number of samples in the ith class Ci , let Mt be the mean of the whole data set, mi be the mean of the ith class Ci, the between- class scatter matrix is defined by: SB=∑ N୧ ୡ ୧ୀଵ ሺmi െ Mtሻ ሺmi െ MtሻT (10) And the within-class scatter matrix is defined by
  6. 6. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 31 Sw=∑ ∑୫୩‫א‬ୡ୧ ୡ ୧ୀଵ ሺmk െ miሻ ሺmk െ miሻT (11) Then the basis vectors is W= arg max ቀ |WTSB W| |WTS౭ W| ቁ (12) Solving Equation(9) produces a matrix W whose columns are the eigenvectors corresponding to the largest eigenvalues of SW ିଵ SB. These columns are the linear discriminant functions associated with classes as a one function for each class. These functions are stored in the database in order to perform the classification as following: Each input vector ( T) to be classified is multiplied with W matrix as ( V ൌ Tିଵ W ) the resulting vector is the linear scores of the testing data T. The class probabilities are calculated using the softmax transform as: P ൌ ୣ୶୮ ሺVሺ୧ሻ ∑ ୣ୶୮ ሺVሺ୧ሻ౟‫א‬C (13) Where C is the set of classes. Each class represents a person in the data base. The value of P show how much the testing data T is near to a specified class, the higher value is the nearest class so the classification is done. A threshold value P can be designated with in order to reject the unknown or to do misclassification. 4. THE EXPERIMENTS The developed face recognition method was applied to the ORL database. Five experiments were conducted. Each with different partitioning scenario to the data set and the performance was evaluated against the number of eigenvectors used see figure (5). The set of eigenvectors is {10,20,25,30,35,40,45,50,55,60}. The set of directions (angles) used for radon transform is shown in table (2). The five scenarios are: a. Scenario #1. In this scenario the ten images for each person are divided as 5 images for training and 5 images for testing. The images were randomly selected. The maximum recognition rate was 93% that is when 25 eigenvectors are selected. See figure (5). The Boxplot is shown in figure (6). It is appear that the median is 90.5%, and the 75 th percentile is around 92.5%. b. Scenario #2. In this scenario the ten images for each person are divided as 9 images for training and one image for testing. The images were randomly selected. The maximum recognition rate was 97.5% that is when 35 eigenvectors are selected. See figure (5). See Boxplot at figure (6). It appears that the median is 95%, and 75 th percentile around 97%. c. Scenario #3. In this scenario the ten images for each person are divided as 8 images for training and 2 images for testing. The images were randomly selected. The maximum recognition rate was 97.5% that is when 35 eigenvectors are selected. See figure (5). See Boxplot at figure (6). It appears that the median is 95%, and 75 th percentile around 97.2%. d. Scenario #4. In this scenario the ten images for each person are divided as 7 images for training and 3 images for testing. The images were randomly selected. The maximum recognition rate was 97.5% that is when 50 eigenvectors are selected. See figure (5). See Boxplot at figure (6). It appears that the median is 96.7%, and 75th percentile around 96.7%.
  7. 7. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 32 e. Scenario #5. In this scenario the ten images for each person are divided as 6 images for training and 4 images for testing. The images were randomly selected. The maximum recognition rate was 95.63% that is when 60 eigenvectors are selected. See figure (5). See Boxplot at figure (5). It appears that the median is 94.4%, and 75 th percentile around 94.9%. 5. DISCUSSION In this work the using of Radon transform improves the performance of PCA+LDA techniques in face recognition. That is if compared with mentioned literature [3, 5, 7, 8, 10, and 13]. The using of PSO for selecting the best directions ( angles) used by Radon transform give better performance as compared to [ 7,9]. This means that the subset selected using PSO is better than the one selected in [7]. From the different scenarios conducted it appears that the performance is improved with the increased number of images per person in the training set this is clear by scenario #2 ,#3,#4 . From Boxplot in figure (7), which shows the performance against the number of eigenvectors used over all scenarios in our experiment, it is clear that the number of eigenvectors between (30-40) gain the good performance. It is also clear that the (35) eigenvectors is the best. 6. CONCLUSIONS A Face Recognition method has been described in this work. The core of this work is to apply the PCA+LDA in Radon space rather than directly to the images. The images are transformed using Radon Transform with a specified angles (directions) set determined using PSO in order to achieve good recognition rate with less computation expensive. The Radon transform used in this method was FFT based. The full range Radon transform is computational expensive if it is performed for angles from 0 degree to 180 degree and for a large number of offsets. To reduce the computations required a subset of angles and offset must be selected. So the PSO was used to select that subset and maintaining a good recognition rate. This method was verified on ROL data base using five different scenarios for training set selection. The best recognition rate was 97.5% when only 35 eigenvectors are used. The number of eigenvectors determines the length of the signature vector that be used for each person in the data base. The recognition rate and the size of signature that represent each person as well as the computation of Radon transform that a achieved in this method is better than the related works stated in the literature review in section 2. 2 : Samples from ORL Database
  8. 8. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 33 TABLE 1 : angles calculated using PSO N=60 TABLE 2: angles calculated using PSO N=10 TABLE 3: angles calculated using PSO N=32 77 angles calculated using PSO N=60 2 4 11 19 21 23 26 28 29 35 36 39 40 41 42 43 44 46 47 51 52 57 58 59 61 62 65 68 71 73 75 79 80 81 83 84 85 89 90 92 93 95 96 98 99 100 106 108 111 112 119 120 122 126 131 134 124 125 126 130 132 134 135 137 135 140 141 144 145 146 149 155 156 161 162 174 178 84 angles calculated using PSO N=10 1 6 8 10 11 12 14 15 17 20 25 28 30 32 33 35 47 49 52 53 54 56 58 59 60 61 62 63 64 68 69 70 71 72 73 75 79 80 84 85 92 95 96 98 103 104 105 108 109 110 114 115 116 119 121 122 124 125 126 130 132 134 135 137 138 142 143 146 151 152 153 154 156 159 161 166 168 169 170 171 172 173 175 179 88 angles calculated using PSO N=32 1 3 4 6 10 11 16 23 24 25 26 27 28 31 32 33 34 35 36 38 42 43 46 47 48 51 52 53 55 57 58 60 61 62 64 73 79 82 86 87 89 91 92 97 98 99 100 101 103 106 107 108 109 112 118 119 120 121 122 123 124 125 126 128 129 134 136 140 141 142 145 147 149 150 151 152 153 156 158 162 163 164 166 168 171 175 176 177
  9. 9. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 34 FIGURE 4 :FFT Based Radon Transform using 90 angles FIGURE 3: FFT Based Radon for an image transform for an image calculated using PSO FIGURE 5: Performance against #of eigenvectors for different scenarios. FIGURE 6: Box Plot show the performance for each scenario. 10 15 20 25 30 35 40 45 50 55 60 80 82 84 86 88 90 92 94 96 98 100 Number of Eign Vectors RecognitionRate% Scenario#1 Scenario#2 Scenario#3 Scenario#4 Scenario#5 80 82 84 86 88 90 92 94 96 98 100 1 2 3 4 5 Data Partitioning Scenario RecognitionRate% The 5 Scenarios performance Box Plot θ (degrees) x' 20 40 60 80 10 20 30 40 50 60 70 80 90 100 110 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 x 10 4 θ (degrees) x' 0 20 40 60 80 100 120 140 160 20 40 60 80 100 2000 4000 6000 8000 10000 12000 14000 16000 18000
  10. 10. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 35 FIGURE 7: Box plot shows the performance against #of eigenvector cross the 5 scenarios. 7. REFERENCES [1] Nilima B. Kachare, Vandana S. Inamdar, 2010, " Survey of Face Recognition Tecchniques", International Journal of Computer Applications(0975-8887), Volum 1-No.19,2010. [2] Patil A.M., Kolhe S.R. and Patil P.M., 2010,"2D Face Recognition Techniques:A Survay", International Journal of Machine Intelligence. [3] Thomas Heseltine, Nick Pears,Jim Austin,Zezhi Chen, 2003, "Face Recognition: A Comparison of appearance-Based approaches", Proc.VIIth Digital Image Computing :Techniques and Applications.,Sun C., Talbot H.,Ourselin S. and Adriaanen T. (10-12 Dec,2003,Sydny). [4] M. Chandra Mohan, V. Vijaya Kumar,K.V.Subbaiah,(2010)," A New Method of Face Recognition Based on Texture Feature Extraction on Individual Components of Face",International Journal of signal and Image Processing (Vol 1-2020/ISS.2)pp.69-74. [5] P.Abouzar, Yousefi,S.K.Setarehdan,(2007), "Hybrid WT Based-DCT Based Face Recogntion" , 2007 IEEE International Conference on Signal Processing and communications(ICSPC 2007). 24-27 November 2007, Dubai,United arab Emirates. [6] Zhan Shi, Minghui Du, Rongbing Huang,(2010),"A Trace Transform based on subspace method for Face Recognition", 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). [7] Laika Karsili and Adnan Acan,2007,"A Radon Transform and PCA Hybrid for High Performance Face Recognition", IEEE International Symposium on Signal Processing and Information Technology. [8] Jamal A hmad Dargham et al. (2010) "Radon transform for face recognition", Artif Life Robotics(2010) 15:359-362,ISAROB 2010. [9] ZHANG Yuhua,WANG Xin,(2010),"Study of Finite Radon Transform in Face Recognition",2010 Second International Conference on Computer Modeling and Simulation. [10] Ergun Gumus, et al., "Eigenfaces and Support Vector Machine Approaches for Hybrid Face Recognition", The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol(2)- No.4. 10 15 20 25 30 35 40 45 50 55 60 82 84 86 88 90 92 94 96 98 100 Number of Egine vectors RecognitionRate%
  11. 11. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 36 [11] Zhang Lin,et al. "Infrared Face Recognition Based On Radon and Multiwavelet Transform" ,Proceedings of ICCTA 2009. [12] Yuehui Chen, Shuyan Jiang, Ajith Abraham, " Face Recognition Using DCT and Hybrid Flexible Neural Tree",2005IEEE,Development Program of Shandong under contract number SDSP2004-0720-03. [13] Jian Zhang,Xiany un Fei, " A New Method for Face Recognition Based on PCA Optimize Strategy"; 2010 International Conference on Computer Application and System Modeling (ICCASM)2010. [14] Dattatr V.Jadhao, Raghunath S.Holambe; "Feature Extraction and Dimensionality Reduction Using Radon and Fourier Transform with Application to Face Recognition", International Conference on Computational Intelligence and Multimedia Application 2007. [15] Rabab M. Ramadan and Rehab F. Abdel Kader; " Face Recognition Using Particle Swarm Optimization-Based Selected Features", International Journal of Signal Processing, Image Processing and Pattern Recognition Vol. 2, No. 2, June 2009. [16] Daming Shi. , Liying Zheng, and Jigang Liu," Advanced Hough Transform Using A Multilayer Fractional Fourier Method", IEEE Transactions on Image Processing, VOL, 19. NO, 6, JUNE 2010. [17] Patrick Etyngier et al., "Radon Space and Adaboost for Pose Estimation", Proceedings of the 18 th International Conference on Pattern Recognition (ICPR'06) 2006 . [18] Mahmoud R.HEJAZI and YO Sung HO," Texture Analysis Using Modified Discrete Radon Transform", IEICE TRANS.INF. & SYST., VOL.E90-D, NO.2 FEBRUARY 2007. [19] S. Venturras, I. Flaounas ," Study of Radon Transformation and Application of its Inverse to NMR", Paper for " Algorithms in Molecular Biology" Course Assoc Prof. I. Emiris, 4 July, 2005. [20] Ming Jiang,Chih ting Wu," Wavelet Based Local Tomography" Mathematical Methods in Medical Imaging , Final Project, Math-6792 Spring 2003. [21] Jiangsheng You, Weiguo Lu, et al; " Image Maching for translation, rotation and uniform scaling by the Radon Transform",1998 IEEE. [22] Alec Banks, et al. " A review of particle swarm optimization. Part II: hybridization, combinatorial, multicriteria and constrained optimization, and indicative applications", Nat Comput (2008) 7:109-124, DOI 10.1007/s11047-007-9050-z. [23] Shih wei Lin and shih chieh Chen, " PSOLDA: A particle swarm optimization approach for enhancing classification accuracy rate of linear discriminant analysis", Applied Soft Computing 9 (2009) 1008-1015. [24] Millie Pant et al, "A New Quantum Behaved Particle Swarm Optimization",GECCO'08,July 12-16, 2008 Atlanta, Georgia. USA. [25] Leandro dos Santos Coelho," A quantum particle swarm optimizer with chaotic mutation operator", Chaos, Solutions and Fractals 37 (2008) 1409-1418.
  12. 12. Hamid M. Hasan, Prof. Dr. Waleed A. AL.Jouhar & Dr. Majed A. Alwan International Journal of Image Processing (IJIP), Volume (6) : Issue (1) : 2012 37 [26] O. Togla altinoz, et al. " Chaos Particle Swarm Optimization PID Controller for the Inverted Pendulum System", 2nd International Conference on Engineering Optimization, September 6- 9, 2010, Lsbon, Portugal. [27] Leandro dos Santos Coelho and Viviana Cocco Mariani, " A novel chaotic particle swarm ooptimization approach using Henon map and implicit filitering local search for load dispatch", Chaos, Solutions and Fractals 39(2009) 510-518. [28] Qing Zhang, et al. " Fast Multi swarm Optimization with Cauchy Mutation and Crossover operation", Puplications of China University of Geosciences, School of Computer, Wuhan, P.R.China, 430074. [29] Yanjun Yan and Lisa ann Osadciw, "Varying Dimensional Particle Swarm Optimization", 2008 IEEE swarm Intelligence symposim , St. Louis Mo USA, September 21-23,2008. [30] R. V. Kulkarni and G.K. Venayagamoorthy, " An Estimation of Distribution Improved Particle Swarm Optimization Algorithm", ISSNIP 2007. [31] Yanj Yan, Ganapathi Kamath and Lisa ann Osadciw, " Feature Selection Optimization by Discrete Particle swarm Optimization for Face recognition", Syracuse University , Syracuse , NY, USA 13244. [32] Hong Pan, LiangZhengXia, and Truong Q.Nguyen," Robust Object detection Scheme using feature selection", Proceeding of 2010 IEEE 17 th International Conference on Image Processing , September 26-29, 2010, Hong Kong. [33] Osslan Osiris Aergara Villegas and Viancy Guadalupe," a Novel Evolutionary Face algorithm Using Particle Swarm Optimization ", 2009 Fith International Conference on Signal Image Technology and Internet Based Syetems. [34] Lanzarini Laura , et al. " Face Recognition Using SIFT and Binary PSO Descriptors", 2010 Proceedings of the ITI 2010 32th Int. Conf. on Information technology Interfaces, June 21- 24,2010, Cavtat, Croatia. [35] Rajinda Senaratne, et al. " Face Recognition by Extending Elastic Bunch Graph Matching with Particle Swarm Optimization", Journal of Multimedia , VOL. 4, No. 4, August 2009. [36] Ming Li, et al. " Application of Improved CPSO-SVM Approach in Face Recognition", 2009 Internaltional Conference on Artificial Intelligence and Com[utational Intelligence. [37] Xiaorong Pu, Zhang YI, Zhongjie Fang," Holistic and partial facial features fution by binary particle swarm optimization", Neural Comput & Applic (2008) 17:481-488. [38] Belhumeur PN, Hespanala JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711-720.

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